Recent improvements in satisfiability algorithms for propositional logic have made partial instantiation methods for first order predicate logic computationally more attractive. Two such methods have been proposed, one by R. Jeroslow and a hypergraph method for datalog formulas by G. Gallo and G. Rago. We show that they are instances of two general approaches to partial instantiation, and we develop these approaches for a large decidable fragment of first order logic (the 98 fragment). 1 Introduction The last few years have seen a surge of interest in applying the computational methods of combinatorial optimization to logical inference problems. Most of this effort has been directed toward propositional logic [2, 3, 4, 5, 10, 14, 15, 16, 17, 18, 19, 22] [23, 26] and probabilistic logic [1, 7, 12, 13, 20, 24, 25]. Less work in this area has focused on predicate logic, but it is nonetheless reaching a stage at which it can make a significant contribution to computational methods..